Image display sheet

ABSTRACT

An object is to provide an image display sheet provided for position detection of an object to be observed so as to realize a smooth pseudo moving image. The image display sheet is provided for an object  3000  to be observed for position detection and constituted by laminating a lenticular sheet composed of arrangement of a plurality of cylindrical lenses and an image forming layer, and an image formed on the image forming layer from a convex shape side of the cylindrical lenses of the lenticular sheet is formed to be observable as virtual image provided with movement, or movement and deformation. A plurality of images for observing virtual images for displaying virtual images  104 A,  104 B in association with the cylindrical lenses are formed repeatedly on the image forming layer so as to correspond to the cylindrical lenses respectively one-on-one, an arrangement pitch length in a horizontal direction of the flat convex lenses and a pitch length in a horizontal direction of the image for observing virtual image differs in a range of not more than 10%, and an arrangement pitch length in a vertical direction of the flat convex lenses and a pitch length in a vertical direction of the image for observing virtual image differs in a range of not more than 10%, and the virtual image smoothly moving with respect to displacement of an angle θ at which the object  3000  is visually observed is thereby observed.

FIELD OF THE INVENTION

The present invention relates to an image display sheet, and moreparticularly, to an image display sheet, which is capable of detecting aposition of an object to be observed with respect to a camera using avirtual image with movement based on a cylindrical lens or flat convexlens and an image.

BACKGROUND TECHNOLOGY

There is known a method of recognizing positional relationship betweenan object to be observed and a robot by photographing the object to beobserved by the camera provided for a head portion or a hand of a robotand detecting the position of the object to be observed with respect tothe camera, or the position of the camera with respect to the object tobe observed. For example, there is provided a method for detecting suchposition by photographing a rod-shaped projection provided for theobject to be observed by a camera provided for the robot and thenanalyzing an image of the projection in the photographed image. Inaddition, there is also provided a method of analyzing the position ofthe robot using an infrared sensor.

In the meantime, there is provided an image display sheet in which animage can be observed as a virtual image such as moving, changing andlike with movement, or movement and deformation by utilizing visualsense of an observer. The image display sheet is composed of alenticular sheet which is constituted by an arrangement of a pluralityof cylindrical lenses and an image forming layer.

FIGS. 26A and 26B are views for explaining a conventionally known imagedisplay sheet, in which FIG. 26A is a perspective view explaining abasic characteristic of a lenticular, and FIG. 26B is an illustratedview for explaining a basic principle of the lenticular.

A lenticular sheet 5001 is composed of cylindrical lenses 5002 and animage forming layer 5003 disposed on a surface opposite to a surfaceformed so as to provide a convex shape so that an image can be observedfrom a lens side in a pseudo moving manner. In an arrangement in shapeof stripe of divided image 5004A to 5004D, a changing image in which animage is observed as if it changes by changing a stereoscopic image orviewing angles of the observer (right eye and left eye of the observer5006 and 5007).

FIG. 27 is for explaining a conventionally known image display sheet5009, in which (A) is a view for explaining a section of aconventionally known image sheet 5009, and (B) is a plan view of theimage forming layer 5003. On the image forming layer 5003 formed to animage forming medium 5008, a plurality of original picture A, B, C, Dare divided into stripe shape. FIG. 27 is an example in which the imagefor right eye 5004 and the image for left eye 5005 are divided each atpredetermined width with respect to the respective lenses. When moving aline of sight (visual line of an observer), an A-image is observed at acertain position, a B-image is observed at another certain position, aC-image is observed at a further certain position, and a D-image isobserved at a further certain position, as if the image is moved bychanging the viewing (observing) angles of an observer.

Further, the Patent Document 1 discloses a technology in which when aplurality of original images are divided into stripe shape to form onesheet of images so as to create images which are observed as if theyhave different pictures as viewed from different viewing angles,boundary of a pitch of a convex lens and divided boundary of the imageis made coincident with each other.

In the meantime, the Patent Document 2 discloses a technology in whichan image for right eye of an observer and an image for left eye of theobserver are divided into strip-shaped pieces each having apredetermined width with respect to each lens, and then, by arrangingthe divided pieces in interlace shape, a pseudo variable image isobserved.

PRIOR ART DOCUMENT Patent Document

-   Patent Document 1: Japanese Patent Laid-open Publication No.    2003-344807-   Patent Document 2: Japanese Patent Laid-open Publication No.    2010-044213

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

In a method in which it is required to detect a position of an object tobe observed by providing a projection to the object to be observed,there is a problem such that position detecting performance decreases ata position in the vicinity of a front surface of the projection.Although such performance can be improved by using a long projection orfine projection, the long projection may obstruct an operation of arobot and the fine projection requires increased space of the locationof such fine projection. In addition, since the projection has a weightitself, it is not available in a case when the projection is used for along time by, for example, bonding it to a wall surface, which furtherrequires several times of maintenance, thus being inconvenient andtroublesome. Furthermore, since the projection requires some space forlocation, which will obstacle the operation or working, and in anadverse case, such as colliding to the projection, it may be broken orsome accidents may be caused. Moreover, in a case of position detectionusing an infrared sensor, an infrared system is expensive, requiringmuch cost, thus also providing a problem.

Incidentally, as a visual effect such as moving or changing using alenticular is an observation of a single image with in an observationalperspective of a constant range and an observation of a next imageexceeding the constant range by varying the observational perspectiveangle. As mentioned above, according to the variation (changing) of theobserving angles, different images are sequentially observed.

At this time, the images observed sequentially according to the changingof the observing angles design an appropriate animated expression withaction, magnification, reduction deformation of human, animal or like,and in such case, an visual effect such as if a motion picture isobtainable.

In an image display sheet in a conventional technology, a virtual imageof an eye can be observed. However, as the line of sight is changed bychanging the viewing angles, the images are observed as ifframe-by-frame advance. Thus, such images are not taken as smooth motionfor an observer, and in a certain case, virtual images are observedintermittently, which will give a sense of discomfort to the observer,thus being inconvenient.

An object of the present invention in consideration of the circumstancesencountered in the conventional technologies mentioned above, is toprovide image display sheet capable of realizing smooth pseudo movingimage and capable of requiring no additional maintenance if once set,with thin and light shape as well as cheap cost.

Means for Solving the Problem

An image display sheet according to the present invention is providedfor an object to be observed for position detection and constituted bylaminating a lenticular sheet composed of arrangement of a plurality ofcylindrical lenses and an image forming layer, and an image formed onthe image forming layer from a convex shape side of the cylindricallenses of the lenticular sheet is formed to be observable as virtualimage provided with movement, or movement and deformation, wherein aplurality of images for observing virtual images for displaying singleor a plurality of the virtual image in association with the cylindricallenses are formed repeatedly on the image forming layer so as tocorrespond to the cylindrical lenses respectively one-on-one, anarrangement pitch length of the cylindrical lenses and a pitch length ofthe image for observing virtual image formed repeatedly on the imageforming layer differs in a range of not more than 10%, and the virtualimage smoothly moving with respect to displacement of an angle at whichthe object is visually observed is thereby observed.

An image display sheet according to the present invention is providedfor an object to be observed for position detection and constituted bylaminating a flat convex lens sheet composed of arrangement of aplurality of flat convex lenses and an image forming layer, and an imageformed on the image forming layer from a convex shape side of the flatconvex lenses of the flat convex lens sheet is formed to be observableas virtual image provided with movement, or movement and deformation,wherein a plurality of images for observing virtual images fordisplaying single or a plurality of the virtual image in associationwith the flat convex lenses is formed repeatedly on the image forminglayer so as to correspond to the flat convex lenses respectivelyone-on-one, an arrangement pitch length in a horizontal direction of theflat convex lenses and a pitch length in a horizontal direction of theimage for observing virtual image formed repeatedly on the image forminglayer differs in a range of not more than 10%, and an arrangement pitchlength in a vertical direction of the flat convex lenses and a pitchlength in a vertical direction of the image for observing virtual imageformed repeatedly on the image forming layer differs in a range of notmore than 10%, and the virtual image smoothly moving with respect todisplacement of an angle at which the object is visually observed isthereby observed.

The image display sheet may be provided with a reference guide that isobservable from a side having convex shape of the cylindrical lens or aside having convex shape of the flat convex lens.

It may be preferred that a plurality of virtual images having at leastone characteristic of different moving amount or different movingdirection with respect to the displacement of an angle at which theobject is visually observable is observable.

It may be preferred that a plurality of virtual images having at leastone characteristic of different shape and different color is observable.

Effect of the Invention

According to the image display sheets for position detection of thepresent invention, a pseudo moving image capable of being smoothlymovable is realized, and the image display sheets capable of reducingfeeling of strangeness is also realized.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an image display sheet according to anembodiment of the present invention.

FIG. 2 is an illustration for explaining structure of the image displaysheet according to the present embodiment, in which (A) is anexplanatory view of a section of a lenticular sheet, and (B) is a planview of an image forming layer.

FIG. 3 is a plan view of the image display sheet according to thepresent embodiment.

FIG. 4 is an explanatory view of a virtual image according to thepresent embodiment.

FIG. 5 is an illustration for explaining structure of the image displaysheet according to another embodiment 1.

FIG. 6 is an illustration for explaining a pitch length measurement ofan image 6 b.

FIG. 7 is an explanatory view of a virtual image according to anotherembodiment 1.

FIG. 8 is a sectional view of an image display sheet according to afurther another embodiment 2.

FIG. 9 is an explanatory view for explaining structure of an imagedisplay sheet according to a further another embodiment 3.

FIG. 10 is a plan view of an image forming layer.

FIG. 11 is a sectional view of an image display sheet according to afurther another embodiment 4.

FIG. 12A is an explanatory view for explaining structure of an imagedisplay sheet according to the further another embodiment 4.

FIG. 12B is a plan view of an image forming layer.

FIG. 13 is an explanatory view of a virtual image according to thefurther another embodiment 4.

FIG. 14 is an explanatory view of a virtual image according to thefurther another embodiment 4.

FIG. 15 is a plan view of an image forming layer of an image displaysheet according to a further another embodiment 5.

FIG. 16A is a plan view of an image forming layer of an image displaysheet according to a further another embodiment 6.

FIG. 16B is a plan view of an image forming layer of an image displaysheet according to the further another embodiment 6.

FIG. 17 is an explanatory view for explaining structure of an imagedisplay sheet according to the further another embodiment 7.

FIG. 18 is an illustrated sectional view of an essential portionrepresenting a focusing process to a lenticular sheet.

FIG. 19A is an explanatory view for explaining structure of an imagedisplay sheet according to a further another embodiment 8.

FIG. 19B is a view explaining an original image 113Xa and an originalimage 113Xb.

FIG. 19C shows a preparation example of an image group for observingstill (stationary) virtual images.

FIG. 19D shows a preparation example of an image group for observingstill virtual images.

FIG. 19E is an illustration for explaining a pitch length measurement ofan image 113 b.

FIG. 20 is an explanatory view for explaining structure of a virtualimage according to a further another embodiment 8.

FIG. 21 is an explanatory view of application example according to thefurther another embodiment 8.

FIG. 22A is a schematic view showing a position detection system S1 towhich an image display sheet according to the present invention is used.

FIG. 22B is a sectional view of an image display sheet 1000.

FIG. 23A is an explanatory view of a camera position and a photographedimage.

FIG. 23B is an explanatory view of a camera position and a photographedimage.

FIG. 23C is an explanatory view of a camera position and a photographedimage.

FIG. 23D is an explanatory view of a camera position and a photographedimage.

FIG. 24A is an example of a photographed image.

FIG. 24B is an example of a photographed image using an image displaysheet having another structure.

FIG. 24 c is an example of a photographed image using an image displaysheet having another structure.

FIG. 24D is an example of an image display sheet having reference guide.

FIG. 24E is an example of an image display sheet having reference guide.

FIG. 25A is a schematic view showing a position detection system S2 towhich an image display sheet according to the present invention is used.

FIG. 26A is a view explaining a basic characteristic feature of alenticular.

FIG. 26B is a schematic explanatory view for explaining a basicprinciple of the lenticular.

FIG. 27 is a view explaining an image display layer forming aconventionally known image display sheet.

MODE FOR EMBODYING THE INVENTION

An image display sheet according to the present invention will bedescribed hereunder with reference to the accompanying drawings. Thedescription will be made in detail as to various embodiments of an imagedisplay sheet which is provided to an object to be detected in position(described hereinlater).

FIG. 1 is a sectional view showing an image display sheet according toan embodiment of the present invention.

An image display sheet 100 is composed of a lenticular sheet 1 and animage forming layer 3 as essential elements. In this embodiment, anexample in which the image forming layer 3 is formed to an image formingmedium such as paper will be explained. Respective layers forconstituting the image display sheet 100 will be explained.

The lenticular sheet 1 is composed of a plurality of cylindrical lenses1 a, 1 a, - - - , 1 a that are arranged in parallel side by side. In theillustration of FIG. 1, the cylindrical lenses 1 a constituting thelenticular sheet 1 are positioned on an upper side. Although a materialforming the lenticular sheet 1 is not limited to a specific one as faras a material has been conventionally used for an image display sheet, atransparent resin material such as PET (polyethylene terephthalate), PP,PETG (grico denatured polyethylene terephthalate), acryl, acrylate groupresin or like.

The image forming medium 2 is provided for the lenticular sheet 1 on aside opposite to the side on which the cylindrical lenses 1 a havingconvex shape are not provided, and the image forming layer 3 is providedon the side of the lenticular sheet 1.

Although a material of the image forming medium 2 is not specificallylimited as far as a material which has been conventionally used is used,paper, as a material of the image forming medium, such as coat (orcoated) paper, synthetic paper, high quality paper, intermediate qualitypaper, impregnated paper, laminate (or laminated) paper, metaldeposition paper, coated paper for printing, coated paper for recordingor like will be used, and also, as a material of the image formingmedium, polyethylene terephthalate film, polyethylene film,polypropylene film polycarbonate film or metal fail, or compositematerial thereof will be used. The material of the image forming medium2 may be appropriately selected in accordance with required strength,usage or like as occasion demands.

The image forming layer 3 is a layer on which images 3 a such aspictures, letters or like as images for virtual image observation isprinted or transferred. The image forming layer 3 is provided on theside of the lenticular sheet 1 of the image forming medium 2. Although amaterial of the image forming layer 3 is not specifically limited, asfar as the material is adhesive to the image forming medium 2, forexample, material for ink, and such material for ink may include lightstorage ink or fluorescent ink.

Further, as the method of laminating the lenticular sheet 1 and theimage forming medium 2 to which the image forming layer 3, there may beperformed by utilizing known adhesion and/or sticking method based onmaterials of the image forming medium 2 and the image forming layer 3 asfar as the laminated layer of the lenticular sheet 1 and the imageforming layer 3 remain transparency. That is, it may be adopted that anobserver (eye E of the observer) can observe the image 3 a formed to theimage forming layer 3 from the convex-shape side of the cylindricallenses of the lenticular sheet 1. More specifically, it may be adoptedthat a virtual image in accordance with movement, or movement anddeformation based on the image 3 a formed to the image forming layer 3can be observed. Furthermore, the image forming layer 3 may be formeddirectly on a surface opposite to the surface on which the cylindricallens 1 a of the lenticular sheet 1 is provided, the detail of which willbe explained hereinafter with reference to FIG. 8.

FIG. 2 includes views for explaining structure or configuration of theimage display sheet according to the present embodiment, in which FIG.2(A) is a sectional view of the lenticular sheet, and FIG. 2(B) is aplan view of the image forming layer. FIG. 3 is a plan view of the imagedisplay sheet according to the present embodiment.

The example shown in FIG. 1 and FIG. 2(A) show a focusing condition ofthe respective cylindrical lenses 1 a in a case where the observer viewsthe cylindrical lenses 1 a from a direction directly above the same at atime when the line of sight of the observer is moved by changing viewingangle of the observer in a direction of a white arrow. Further, in thiscase, focusing surface of the cylindrical lenses 1 a exists on the imageforming layer 3. In other words, the cylindrical lenses 1 a are composedso that their focuses are concentrated on the image 3 a. Further, inactual, the observer can confirm the smooth movement, or movement anddeformation of the virtual image by changing the viewing angle as wellas viewing from a direction directly above the image 3 a.

As shown in FIG. 2(B), a plurality of images 3 a are formed on the imageforming layer 3. In the examples shown in FIGS. 2(A) and 2(B), theimages 3 a are formed repeatedly so as to correspond to the cylindricallenses 1 a, respectively, one-on-one, that is, the images 3 a of sixeyes correspond to the cylindrical lenses 1 a, respectively.

An image display sheet is constructed so that a difference between apitch length A of arrangement of the adjacent cylindrical lenses 1 a anda pitch length B of the adjacent images 3 a satisfies that thedifference is within a range of 0% to 10% with respect to the pitchlength A of the cylindrical lenses 1 a or the pitch length B of theimages 3 a.

In the example of FIG. 2, the image display sheet is constructed so thatthe arrangement pitch length A of the adjacent cylindrical lenses 1 aand the pitch length B of the adjacent images 3 a are different fromeach other and so that the difference between the pitch lengths A and Bis not more than 10%.

In the case the pitch length B of the images 3 a is not more than thearrangement pitch length of the cylindrical lenses 1 a (A>B), thevirtual image 4 based on the cylindrical lenses 1 a and the images 3 awill be observed stereoscopically for the observer in a manner such thatthe virtual image 4 goes down below the lenticular sheet 1. In thiscase, when the line of sight of the observer is moved rightward, thevirtual image 4 is also observed as is moved rightward, and on the otherhand, when the line of sight of the observer is moved leftward, thevirtual image 4 is also observed as is moved leftward. That is, thevirtual image 4 is observed in the same direction as the movingdirection of the line of sight of the observer.

On the other hand, in the case the pitch length B of the images 3 a isnot less than the arrangement pitch length of the cylindrical lenses 1 a(A<B), the virtual image 4 based on the cylindrical lenses 1 a and theimages 3 a will be observed stereoscopically for the observer in amanner such that the virtual image 4 goes up (floats) above thelenticular sheet 1. In this case, when the line of sight of the observeris moved rightward, the virtual image 4 is observed as is movedleftward, and on the other hand, when the line of sight of the observeris moved leftward, the virtual image 4 is observed as is movedrightward. That is, the virtual image 4 is observed in the directionreverse to the moving direction of the line of sight of the observer.

A pitch length “x” of the virtual image 4 shown in FIG. 3 is determinedby the following equation (1). A width “y” of the virtual image 4 in thearrangement direction of the cylindrical lenses 1 a is determined by thefollowing equation (2). The character “A” is the pitch length of thearrangement of the cylindrical lenses 1 a, the character “B” is thepitch length of the images 3 a, the character “C” is a width (lateralsize) of the image 3 a in the direction of the arrangement of thecylindrical lenses 1 a. In addition, height “z” (vertical size) of theimage 3 a in the direction vertical to the arrangement direction of thecylindrical lenses 1 a is the same as a height “D” (vertical size) ofthe image 3 a in the direction vertical to the arrangement direction ofthe cylindrical lenses 1 a (equation (3)).

$\begin{matrix}\lbrack{Equations}\rbrack & \; \\{x = \frac{A^{2}}{{A - B}}} & {{equation}\mspace{14mu} (1)} \\{y = \frac{A \times C}{{A - B}}} & {{equation}\mspace{14mu} (2)} \\{z = D} & {{equation}\mspace{14mu} (3)}\end{matrix}$

As mentioned above, the size of the virtual image 4 observed by theabove equations (1) to (3) can be freely set by appropriately adjustingor changing the pitch length A of the arrangement of the cylindricallenses 1 a, the pitch length B of the images 3 a, the width C of theimage 3 a in the direction of the arrangement of the cylindrical lenses1 a, and the height “D” of the image 3 a.

FIG. 4 is a view explaining the virtual image according to the presentembodiment. As the observer moves while changing his line of sight bychanging the viewing angle, the virtual images based on the images 3 aformed on the image forming layer 3 and the virtual images 4 based onthe images 3 a formed on the image forming layer 3 and the cylindricallenses 1 a are observed.

More specifically, in the case the pitch length B of the images 3 a isnot more than the arrangement pitch length of the cylindrical lenses 1 a(A>B), the virtual image 4 based on the cylindrical lenses 1 a and theimages 3 a will be observed stereoscopically for the observer in amanner such that the virtual image 4 goes down below the lenticularsheet 1. In addition, following the movement of the line of sight of theobserver, the virtual image 4 can be observed as a virtual image movingsmoothly.

On the other hand, in the case when the pitch length B of the images 3 ais not less than the arrangement pitch length of the cylindrical lenses1 a (A<B), the virtual image 4 based on the cylindrical lenses 1 a andthe images 3 a will be observed stereoscopically for the observer in amanner such that the virtual image 4 goes up above the lenticular sheet1. In addition, following the movement of the line of sight of theobserver, the virtual image 4 can be observed as a virtual image movingsmoothly.

In the equations (1) and (2), while the value |A−B| becomes smaller,moving speed with respect to the movement of the line of sight becomesfaster. Therefore, it is preferred that the value |A−B| is determined inaccordance with the use condition of the image display sheet 100, thatis, in view of speed of the movement of the line of sight of the actualobserver. In other words, it is preferred that the moving speed of thevirtual image 4 is set so as to accord with the speed of the line ofsight of the observer.

According to the present embodiment, a plurality of images 3 a fordisplaying the virtual images in relation to the cylindrical lenses 1 aare formed on the image forming layer 3 in a repeated manner so as tocorrespond to the cylindrical lenses 1 a of the lenticular sheet 1,respectively, one-on-one. In addition, the images 3 a are formed suchthat the arrangement pitch length A of the cylindrical lenses 1 a andthe pitch length B of the images 3 a differ from each other, and thedifference between these pitch lengths A and B is not more than 10% withrespect to the arrangement pitch length A of the cylindrical lenses 1 aor the pitch length B of the images 3 a. Accordingly, as a result, theimage display sheet capable of observing the virtual images 4 withsmooth movement, or movement and deformation can be realized. Inaddition, since the image size (width C and height D) of the image 3 aare approximately several tens μm to several tens mm, the image forminglayer 3 can be printed and/or transferred to the image forming medium 2by using a general equipment (for example, general-purpose printingmachine, transferring machine, general-purpose image software and thelike) without using dedicated equipment.

In a case where the lenticular sheet 1 having the arrangement pitchlength A of the cylindrical lenses 1 a is in a range of 330 μm to 345 μmis used, it is preferred that the difference between the arrangementpitch length A of the cylindrical lenses 1 a and the pitch length B ofthe images 3 a differs, by 0.1% to 4%, with respect to the arrangementpitch length A of the cylindrical lenses 1 a or the pitch length B ofthe images 3 a.

Further, although the images 3 a are formed so as to substantiallycorrespond to the cylindrical lenses 1 a, respectively, one-on-one in arepeated manner, since the arrangement pitch length A of the cylindricallenses 1 a and the pitch length B of the images 3 a differ from eachother, the corresponding positions therebetween will gradually shiftfrom each other. Thus, in this meaning, the cylindrical lenses 1 a andthe images 3 a do not correspond actually one-on-one. The differencebetween the arrangement pitch length A of the cylindrical lenses 1 a andthe pitch length B of the images 3 a makes it possible to observe thesmooth virtual images.

(Embodiment of Image Display Sheet)

An embodiment of an actual image display sheet will be describedhereunder, in which design examples of respective portions in a casewhen a virtual image of eye is observed will be explained.

Dimensions of the respective structural portions of the image displaysheet are as follows.

Thickness of lenticular lens 1 a: 0.45 mm

Arrangement pitch length A of cylindrical lenses: 336 μm

Pitch length B of images 3 a: 330 μm

Difference between pitch lengths A and B: 6 μm

Width C of image 3 a: 225 μm

Height D of image 3 a: 12.7 mm

Pitch length x of virtual image: 19 mm

Width y of virtual image 4: 12.7 mm

Height z of virtual image 4: 12.7 mm

Other Embodiment 1

An image display sheet 1 according to another one embodiment 1 has astructure capable of observing one virtual image. Further, descriptionsconcerning the similar structure of the embodiment mentioned above willbe omitted herein.

FIG. 5 is a diagram showing a structure or configuration of an imagedisplay sheet according to the other embodiment 1, in which thecorresponding relationship between respective cylindrical lenses 5 a ofa lenticular sheet 5 and images 6 a, 6 b are shown. FIG. 6 is a viewexplaining a pitch length measurement of the image 6 b. FIG. 7 is a viewexplaining a virtual image according to the other embodiment 1. Further,since the structure or configuration of the lenticular sheet 5 issimilar to the lenticular sheet 1 mentioned hereinabove, the explanationthereof is now omitted herein.

On the image forming layer 6, a predetermined number of images as imagegroup for virtual image observation are formed. The image 6 a near thecenter of the image group is an image having no cutout, and each ofother images 6 b excluding the image 6 a near the center has a cutout 6c on a side of the image 6 a near the central portion. The images 6 aand 6 b are formed so as to correspond to the cylindrical lenses 5 a,respectively, substantially one-on-one.

In an example shown in FIG. 5, the image group is composed totally ofeleven (11) images including one image 6 a near the central portion andten (10) images 6 b having cutouts 6 c. The cutouts 6 c become widerapart from the central image 6 a towards laterally apart direction onthe drawing. Further, although, in FIG. 5, only one image 6 a at thecentral portion is shown, a plurality of images 6 a may be adopted.

The images 6 a and 6 b are formed, as mentioned hereinbefore withreference to the embodiment, so as to substantially correspond to thecylindrical lenses 5 a, respectively, one-on-one. Further, an imagedisplay sheet is constructed so that a ratio of difference between apitch length A of arrangement of the adjacent cylindrical lenses 5 a anda pitch length B of the images 6 a and 6 b satisfies that the differenceis within a range of 0% to 10% with respect to the arrangement pitchlength A of the cylindrical lenses 1 a or the pitch length B of theimages 6 a and 6 b.

It is herein noted that the pitch length B between the images 6 a and 6b and the pitch length B between the images 6 b are deemed as the pitchlength B in a case of supposing that the image 6 b is not provided witha cutout (FIG. 6).

Furthermore, the widths y and z of the observed virtual image will bedetermined on the basis of the equations (2) and (3) describedhereinbefore. The width C and D are ones in a case of supposing that theimages 6 b have no cutout (FIG. 6). In a case when the widths C and Dare obtained from the image 6 b with no cutout, the lateral size of theimage 6 a is determined as the width C and the vertical size thereof isthe height D.

Further, the image forming layer 6 may be formed to an image formingmedium, not shown, and also, as in another embodiment 2 described hereinafter, may be formed directly to the lenticular sheet 5. In the casewhen the image forming layer 6 is formed on the image forming medium,the image forming medium has a structure or configuration identical tothe image forming medium 2 described hereinbefore.

According to the structure mentioned above, an image display sheet 200capable of observing only one virtual image 7 as shown in FIG. 7 can berealized. When a line of sight is being moved by changing a viewer'sobserving angle, one virtual image 7 in which the central image isdistinctively displayed is observed as pseud moving image (graphics)based on the images 6 a and 6 b formed to the image forming layer andthe cylindrical lenses 5 a.

(Embodiment of Image Display Sheet)

An embodiment of an actual image display sheet according to anotherembodiment 1, in which design examples of respective portions in a casewhen a virtual image of eye is observed, will be explained.

Dimensions of the respective structural portions of the image displaysheet are as follows.

Thickness of lenticular lens 1 a: 0.45 mm

Arrangement pitch length A of cylindrical lenses: 336 μm

Pitch length B between images 6 a and 6 b (and between 6 b and 6 b): 330μm

Difference between pitch lengths A and B: 6 μm

Width C of image 6 a (and 6 b): 225 μm

Height D of image 6 a (and 6 b): 12.7 mm

Width y of virtual image 7: 12.7 mm

Height z of virtual image 7: 12.7 mm

Other Embodiment 2

FIG. 8 is a sectional view of an image display sheet according to otherembodiment 2. In this other embodiment 2, an image display sheet 300 hasa structure in which an image forming layer is formed to a lenticularsheet.

As shown in FIG. 8, the image display sheet 300 is provided with alenticular sheet 8 and an image forming layer 9 as essential elements.The structure of the lenticular sheet 8 is the same as that of thelenticular sheet 1 mentioned hereinbefore, so that the descriptionthereof is omitted herein.

The image forming layer 9 is a layer on which images 9 a such aspictures, letters or like as images for virtual image observation isprinted or transferred. The image forming layer 9 is provided on thesurface on the side opposite to the surface on which convex-shapedcylindrical lenses 8 a of the lenticular sheet 8. Although a material ofthe image forming layer 3 is not specifically limited, as far as thematerial is adhesive to the lenticular sheet 8, for example, knownmaterial for ink, and such material for ink may include light storageink or fluorescent ink.

On the image forming layer 9, a plurality of images 9 a are formedrepeatedly so as to substantially correspond to the cylindrical lenses 8a one-on-one. Further, an image display sheet is constructed so that aratio of difference between a pitch length A of arrangement of thecylindrical lenses 8 a and a pitch length B of the images 9 satisfiesthat the difference is not more than 10% with respect to the arrangementpitch length A of the cylindrical lenses 8 a or the pitch length B ofthe images 9. The other structures of the embodiment 2 are similar tothose of the image forming layer 3 or the image forming layer 6, so thatthe explanations thereof are omitted herein. As mentioned above, theimage forming layer 3 or the image forming layer 6 may be formeddirectly to the lenticular sheet 8.

Other Embodiment 3

It may be possible to combine the image display sheet with astereoscopic viewing sheet. As such embodiment in which the imagedisplay sheet is combined with a stereoscopic viewing sheet will beexplained as the other embodiment 3.

FIG. 9 is a view for explaining a structure of an image display sheetaccording to the other embodiment 3. FIG. 10 is a plan view of an imageforming layer. FIG. 9 shows a section of an image display sheet 400,which is composed of a virtual image display portion 40 a and an imagedisplay portion 40 b to be observed.

The virtual image display portion 40 a is composed of the lenticularsheet 10 common to the display portion 40 b of the image to be observed,an image forming medium 11 common to the display portion 40 b of theimage to be observed, and the image forming layer 12. The displayportion 40 b of the image to be observed (image display portion 40 b forobservation) is composed of the lenticular sheet 10 common to thevirtual image display portion 40 a, the image forming medium 11 commonto the virtual image display portion 40 a, and the image forming layer13.

The lenticular sheet 10 has a structure similar to that of thelenticular sheet 1 mentioned above, the image forming medium 11 has astructure similar to that of the image forming medium 2 mentioned above,and the image forming layer 12 has a structure similar to that of theimage forming layer 3 or image forming layer 6 mentioned above, so thatthe explanations thereof will be omitted herein. Further, in examplesshown in FIGS. 9 and 10, images 12 a as images for virtual imageobservation are formed on the image forming layer 12.

The image forming medium 11 is an image forming medium common to thevirtual image display portion 40 a and the image display portion 40 bfor observation. The image forming layers 12 and 13 are formed on theside of the lenticular sheet 10. The other structures of the imageforming medium 11 are substantially identical or similar to that of theimage forming medium 2 mentioned hereinbefore, and accordingly, theexplanation thereof will be omitted herein.

The image display portion 40 b for observation has substantially thesame structure of the conventionally known lenticular display body andattains substantially the same effect as that attained thereby. Theimage forming layer 13 of the image display portion 40 b for observationis a layer on which single or a plurality of other images, differentfrom the image for observing the virtual image (image 12 a in thepresent embodiment) are printed or transferred. The other images mayherein include images for stereoscopic view, images for changing, andimages picture patterns or letters or like as images of animation. Inthe example of FIG. 10, images 13 a for left eye and images 13 b forright eye displaying the images to be observed acting in associationwith the cylindrical lenses 10 a of the lenticular sheet 10 are arrangedin form of stripe. A material for the image forming layer 13 is notspecifically limited as far as it closely adheres to the image formingmedium 11, and for example, a conventionally known ink material or likewill be used.

The lamination of the lenticular sheet 10 and the image forming medium11 is performed by known adhesion method or sticking method inaccordance with materials forming the image forming medium 11 and theimage forming layers 12 and 13 with the transparency of the lenticularsheet 10 and the image forming layers 12 and 13 being maintained.

When an observer moves his (or her) line of sight by changing viewingangle from an upper position of the lenticular sheet 10, a virtual imageis observed on the virtual image display portion 40 a in associatedaction between the image of the image forming layer 12 and thecylindrical lens 10 a, and an image for observing for virtual image isobserved on the image display portion 40 b for observation in associatedaction between the image of the image forming layer 13 and thecylindrical lens 10 a.

As explained hereinabove, according to the present embodiment, the imagedisplay sheet 400 in combination of the virtual image display portion 40a capable of observing the virtual image and the image display portion40 b for observation capable of observing the image to be observed(observed image) can be constructed. Further, it is to be noted thatalthough, in the explanations made with reference to FIGS. 9 and 10, acase of only two virtual image display portions 40 a and three imagedisplay portions 40 b for observation was exemplarily described for thesake of simple and easy understanding, a desired number of (plural orsingle) virtual image display portions 40 a and a desired number of(plural or single) image display portion 40 b for observation may becombined in accordance with the demand of design for the image displaysheets.

According to the image display sheet 400 of the other embodiment 3,since the virtual image display portions 40 a and the image displayportions 40 b for observation are composed of the same image formingmedium 11, a stable image display sheet can be realized more easily. Forexample, in a case when an image display sheet on which a face of“kabuki” actor is displayed will be prepared, both eye portions areformed by the virtual image display portions 40 a and portions otherthan both eyes are formed by the image display portions 40 b forobservation to thereby display the stereoscopic face of the “kabuki”actor in which only both eyes can be smoothly moved.

Further, in FIGS. 9 and 10, the image display portion 40 b forobservation is composed as a conventionally known lenticular displayportion and constructed so that the stereoscopic image to be observedcan be observed by the associated action between the images of the imageforming layer 13 and the cylindrical lenses 10 a. However, the presentinvention is not limited to such structure or configuration, and forexample, a two-dimensional image, such as illustration, image of face,face picture or like, which is not an image attaining a specific effectby such as stereoscopic image or changing image in the associated actionwith a cylindrical lens, may be formed as the image display portion 40 bfor observation. For example, the two-dimensional image may be an imageas a back scene of the virtual image display portion 40 a. For example,in a case of using for position detection, an identification image suchas bar-code, two-dimensional code or like for identifying the imagedisplay sheet to the camera may be utilized. In the case of thetwo-dimensional image, the lenticular sheet 10 may not be provided forthe image display portion 40 b for observation.

Other Embodiment 4

According to the present embodiment, an image display sheet may beformed using a flat convex lens sheet. Hereafter, a case in which a flatconvex lens sheet is used will be explained as the other embodiment 4.

FIG. 11 is a sectional view representing an image display sheet 500according to the other embodiment 4. The image display sheet 500 iscomposed of a flat convex lens sheet 15 and an image forming layer 17 asessential components. Herein, an example in which an image forming layer16 is formed to an image forming medium such as paper will be described.Respective layers constituting the image display sheet 500 will beexplained hereunder.

The flat convex lens sheet 15 is formed by arranging a plurality of flatconvex lenses 15 a in form of honeycomb shape or square shape in a planview. The flat convex lenses 15 a are shown in an upper portion on thedrawing of FIG. 11, for example. Further, although a material for theflat convex lens sheet 15 is not limited to specific one as far as alens sheet which has been conventionally used as an image display sheet,a transparent resin material such as PET (polyethylene terephthalate),PP, PETG (glycol-denatured polyethylene terephthalate), acryl, acrylateseries resin or like.

The image forming medium 16 is disposed on a side of the flat convexsheet 15 on which convex-shape is not formed, and the image forminglayer 17 is formed on the flat convex sheet 15 side of the image formingmedium 16. The other structures of the image forming medium 16 aresubstantially identical to those of the image forming medium 2 mentionedhereinbefore, so that the explanation thereof will be omitted herein.

The image forming layer 17 is a layer formed by printing or transferringan image 17 a of a picture pattern or a letter as an image for virtualimage observation. The image forming layer 17 is provided for the imageforming medium 16 on the side of the flat convex lens. A material forthe image forming layer 17 is not limited as far as the material closelyadheres to the image forming medium 16, and for example, aconventionally known ink material may be utilized. The material for inkmay include light storage ink or fluorescent ink. The other structuresof the image forming layer 17 are substantially identical to those ofthe image forming layer 3 mentioned hereinbefore, so that theexplanation thereof will be omitted herein.

A pint face of the flat convex lens 15 a is on the image forming layer17. In other words, the flat convex lens 15 a is constructed so that afocal point thereof accords with the image 17 a. Further, the laminationof the flat convex sheet 15 and the image forming medium 16 to whichimage forming layer 17 is provided is performed by a known adhesionmethod or sticking method in accordance with materials forming the imageforming medium 16 and the image forming layer 17 with the transparencyof the flat convex sheet 15 and the image forming layer 17 beingmaintained. Namely, it may be allowed for the flat convex sheet 15 tohave a structure in which the image 17 a formed to the image forminglayer 17 can be observed by the observer from the side having the convexshape of the flat convex lens 15 a of the flat convex sheet 15. Morespecifically, it may be allowed for the flat convex sheet 15 to have astructure in which a virtual image with the movement, or movement anddeformation based on the image 17 a formed to the image forming layer 17can be observed.

FIG. 12A is a view for explaining a structure of the image display sheetaccording to the other embodiment 4. FIG. 12A is a plan view of the flatconvex lens sheet, and FIG. 12B is a plan view of the image forminglayer. FIG. 13 and FIG. 14 are views for explaining the structure of avirtual image according to the other embodiment 4.

The flat convex sheet 15 is formed with a plurality of flat convexlenses 15 a. FIG. 12A shows an example of the flat convex lens sheethaving honeycomb arrangement. As shown in FIG. 12B, a plurality ofimages 17 a are formed to the image forming layer 17. The images 17 aare formed in a repeated arrangement so as to substantially correspondto the flat convex lenses 15 a, respectively, one-on-one. In theexamples of FIGS. 12A and 12B, images 17 a of thirty (30) eyescorrespond respectively to the flat convex lenses 15 a one-on-one.

The flat convex display sheet is constructed so that a ratio ofdifference between a pitch length of arrangement of the flat convexlenses 15 a and a pitch length of the images 17 a satisfies that theratio of difference is not more than 10% with respect to the pitchlength of the flat convex lenses 15 a or the pitch length of the images17 a. In the examples of FIGS. 12A and 12B, the transverse arrangementpitch length A₁ (in figure) of the flat convex lenses 15 a (horizontaldirection) and the transverse pitch length B₁ of the images 17 a differfrom each other, and the ratio of difference is not more than 10% withrespect to the pitch length A₁ of the flat convex lenses 15 a or thepitch length B₁ of the images 17 a. In addition, the verticalarrangement pitch length A₂ (in figure) of the flat convex lenses 15 a(vertical direction) and the vertical pitch length B₂ of the images 17 adiffer from each other, and the ratio of difference is not more than 10%with respect to the pitch length A₂ of the flat convex lenses 15 a orthe pitch length B₂ of the images 17 a.

That is, in a case where the pitch length B₁(B₂) of the images 17 a issmaller than the arrangement pitch A₁(A₂) of the flat convex lenses 15 a(A₁>B₁ and A₂>B₂), the virtual image 18 based on the flat convex lenses15 a and the images 17 a will be observed stereoscopically for theobserver in a manner such that the virtual image 18 goes down below theflat convex lens sheet 15. In this case, when the line of sight of theobserver is moved rightward, the virtual image 18 is observed as is alsomoved rightward, and on the other hand, when the line of sight of theobserver is moved leftward, the virtual image 18 is observed as is alsomoved leftward. That is, the virtual image 18 is observed in the samedirection as the moving direction of the line of sight of the observer.

On the other hand, in the case the pitch length B₁ (B₂) of the images 17a is not less than the pitch length A₁ (A₂) of the arrangement of theflat convex lenses 15 a (A₁<B₁ and A₂<B₂), the virtual image 18 based onthe flat convex lenses 15 a and the images 17 a will be observedstereoscopically for the observer in a manner such that the virtualimage 18 goes up above the flat convex lens 15. In this case, when theline of sight of the observer is moved rightward, the virtual image 18is observed as is moved leftward, and on the other hand, when the lineof sight of the observer is moved leftward, the virtual image 18 isobserved as is moved rightward. That is, the virtual image 18 isobserved in the direction reverse to the moving direction of the line ofsight of the observer.

Further, in order to observe the virtual image moving smoothly, it maybe preferred to take construction in a manner such that, in a case wherethe arrangement pitch length A of the flat convex lens 15 a is in arange of 195 μm and 180 μm, a ratio of difference between thearrangement pitch length A of the flat convex lens 15 a and the pitchlength B of the image 17 a differs in a range of 0.01% and 5%. In a morespecific explanation along the difference in the line of sight movement,in order to observe the virtual image 18 moving smoothly, it may bepreferred that the pitch length B of the image 17 a is in a range of99.99% to 95.00% of the arrangement pitch length A of the flat convexlens 15 a, and more preferably, in a range of 99.50% to 97.00% thereof.Further, in order to observe the virtual image 18 moving in a directionreverse to moving direction of the line of sight, it may be preferredthat the pitch length B of the image 17 a is in a range of 100.01% to105.00% of the arrangement pitch length A of the flat convex lens 15 a,and more preferably, in a range of 100.50% to 103.00% thereof.

As shown in FIGS. 13 and 14, as an observer changes his (her) line ofsight by changing the viewing angle, the virtual image 18 based on theimage 17 a formed to the image forming layer 17 and the flat convex lens15 a can be observed from an upper side. FIG. 13 shows a state of thevirtual image in a case where the line of sight is moved in a horizontaldirection, and FIG. 14 shows a state of the virtual image in a casewhere the line of sight is moved in a vertical direction.

A pitch length “x₁” of the virtual image 18 shown in FIG. 13 isdetermined by the equation (1). A width “y₁” of the virtual image 18 inthe horizontal direction is determined by the equation (2). Herein, thecharacter “A” is the pitch length A₁ of the arrangement of the flatconvex lenses 15 a, the character “B” is the pitch length B₁ of theimages 17 a in the horizontal direction, the character “C” is a width C₁(lateral size) of the image 17 a in the horizontal direction of theimages 17 a.

A pitch length “x₂” of the virtual image 18 shown in FIG. 14 isdetermined by the equation (1). A width “y₂” of the virtual image 18 inthe vertical direction is determined by the equation (2). Herein, thecharacter “A” is the pitch length A₂ of the arrangement of the flatconvex lenses 15 a, the character “B” is the pitch length B₂ of theimages 17 a in the vertical direction, the character “C” is a height C₂(vertical size) of the image 17 a in the vertical direction of theimages 17 a.

Further, in the equations (1) and (2), while the value |A−B| becomessmaller, the moving speed with respect to the movement of the line ofsight of the observer becomes faster. Therefore, it is preferred thatthe value |A−B| is set in accordance with the use condition of the imagedisplay sheet 500, that is, in view of speed of the movement of the lineof sight of the actual observer. In other words, it is preferred thatthe moving speed of the virtual image 18 is set so as to accord with thespeed of the line of sight of the observer when the observer observesthe virtual image 18 by moving his (her) line of sight.

According to the structures mentioned above, the image display sheetfrom which the smoothly moving virtual images can be observed by usingthe flat convex lens sheet. As the observer moves his (her) line ofsight by changing the viewing angle, the virtual image 18 based on theimages 17 a formed to the image forming layer 17 and the flat convexlenses 15 a.

Further, in the described embodiment, although the image forming layer17 is formed to the image forming medium 16, the image forming layer 17may be formed directly on a surface opposite to the surface to which theflat convex lens of the flat convex lens sheet 15 as being made withreference to the other embodiment 2 described hereinbefore. Moreover,the image display sheet 500 may be constructed so that the images to beobserved can be observed by the function based on the combination with aconventionally known stereoscopic viewing sheet with reference to theother embodiment 3 and the stereoscopic image, changing image, oranimation image, or combination thereof. In such case, the images 17 afunction as images for the virtual image observation.

Furthermore, the image display sheet 500 may form an image display sheetfor observing one virtual image on the basis of the other embodiment 1,which may be explained hereunder as the other embodiment 5.

Other Embodiment 5

An image forming layer in a case where only one virtual image isobserved by using a flat convex lens sheet will be explained. It isfurther to be noted that a flat convex lens sheet and an image formingmedium have the same or similar structures as those of the otherembodiment 4.

FIG. 15 is a plan view representing an image forming layer of an imagedisplay sheet according to the other embodiment 5.

Predetermined number of images 19 a and 19 b as image group for virtualimage observation are formed on an image forming layer 19. An image 19 adisposed near a central portion of the image group is an image having nocutout, and other images 19 b than the central one 19 a each has acutout 19 c on the central image 19 a side. The images 19 a and 19 b areformed so as to substantially correspond to a flat convex lens, notshown, one-on-one.

In the embodiment shown in FIG. 15, the image group is composed of theimage 19 a formed near the central portion of the image forming layer 19and a plurality of images 19 b having cutouts 19 c. The cutout 19 c ofthe image 19 b becomes lager as the location of the images 19 b becomesapart from the central image 19 a. Further, in the example of FIG. 15,although one image 19 a near the central portion is referred to, aplurality of images 19 a may be formed near the central portion of theimage forming layer 19.

The flat convex display sheet is constructed so that a arrangement pitchlength of the flat convex lenses and pitch lengths of the images 19 aand 19 b differs and a ratio of difference between the arrangement pitchlength of the flat convex lenses and the pitch lengths of the images 19a and 19 b satisfies that the ratio of difference is not more than 10%with respect to the pitch length of the flat convex lenses or the pitchlength of the images 19 a and 19 b. Specifically, it is constructed thatthe transverse arrangement pitch length A₁ of the flat convex lenses(horizontal direction) and the transverse pitch length B₁ of the images19 a differ from each other so that the ratio of difference therebetweenis not more than 10% with respect to the pitch length A₁ of the flatconvex lenses or the pitch length B₁ of the images 19 a. In addition,the vertical arrangement pitch length A₂ of the flat convex lenses inthe vertical direction and the vertical pitch length B₂ of the images 19a differ from each other so that the ratio of difference is not morethan 10% with respect to the pitch length A₂ of the flat convex lensesor the pitch length B₂ of the images 19 a. Further, the pitch length B₁and B₂ between the image 19 a and the image 19 b, and the pitch lengthB₁ and B₂ between the images 19 b are supposed to the pitch length B₁and B₂ between the images 19 b in a case of no formation of cutout 19 cto the image 19 b.

A pitch length “x₁” of the virtual image, not shown, in the horizontaldirection is determined by the equation (1). A width “y₁” of the virtualimage in the horizontal direction is determined by the equation (2).Herein, the character “A” is the pitch length A₁ of the arrangement ofthe flat convex lenses, the character “B” is the pitch length B₁ of theimages 19 a and 19 b in the horizontal direction, the character “C” is awidth C₁ (lateral size) of the image 19 a and 19 b in the horizontaldirection.

A pitch length “x₂” of the virtual image, not shown, in the verticaldirection is determined by the equation (1). A width “y₂” of the virtualimage in the vertical direction is determined by the equation (2).Herein, the character “A” is the pitch length A₂ of the arrangement ofthe flat convex lenses, the character “B” is the pitch length B₂ of theimages 19 a and 19 b in the vertical direction, the character “C” is aheight C₂ (vertical size) of the image 19 a and 19 b in the verticaldirection.

According to the structure explained hereinbefore, the image displaysheet capable of observing only one virtual image smoothly moving byusing the flat convex lenses can be realized. As a viewing line (line ofsight) of the observer moves by changing the viewing angle of theobserver, one virtual image, in which the central image is extremelyremarkably displayed, can be observed based on the images 19 a, 19 bformed on the image forming layer 19 and the flat convex lenses.

It is further to be noted that the above-mentioned embodiments may beexecuted by respectively combining them. For example, as to the otherembodiment 3, the image forming layer may be directly formed on thesurface opposite to the surface on which convex shape of the cylindricallens of the lenticular sheet is formed in accordance with the othersecond embodiment. Furthermore, as to the other embodiments 4 and 5, theimage forming layer may be directly formed on the surface opposite tothe surface having the convex shape of the flat convex lenses of theflat convex lens sheet in accordance with the other second embodiment.

In the embodiments described above, although the examples are explainedwith the eye is an image for observing a virtual image (an image forobserving virtual image), virtual images based on images of variouspicture patterns, letters and the like without limiting to the eyes canbe observed. Especially, as an image for observing a virtual image, byusing images of opened eye and closed eye, a virtual image withvariation of opening/closing eyes can be observed. Moreover, variouskinds or modes of virtual images with motion and variation can berealized by forming mouth opening/closing images or floweropening/closing images, or the like as images for observing virtualimage. Hereunder, a case in which an image of an arrow is made as animage for observing virtual image will be explained with reference toFIG. 16.

Other Embodiment 6

FIGS. 16A and 16B are plan views representing an image forming layer ofan image display sheet according to the other embodiment 6. FIGS. 16Aand 16 b are examples of the image forming layer in which arrows aremade as virtual image observation image.

On an image forming layer 20 shown in FIG. 16A, a plurality of images 20a are formed as images for observing virtual images. The images 20 a areformed in a repeated manner so as to be coincident with the cylindricallenses, not shown, of the lenticular sheet approximately one-on-onearrangement. The arrangement pitch length of the cylindrical lenses andthe pitch length B of the images 20 a are made to be different so thatthe ratio of difference therebetween is not more than 10% with respectto the arrangement pitch length of the cylindrical lenses or pitchlength B of the images 20 a. Further, the image forming layer 20 may beformed to an image forming medium, not shown, or formed directly on thelenticular sheet as in the other embodiment 2. In the case where theimage forming layer 20 is formed on the image forming medium, the imageforming medium may have a structure substantially the same as oridentical to the image forming medium 2 mentioned hereinbefore.

A virtual image showing an arrow based on the image 20 a and thecylindrical lenses are observed from the upper side as a pseudo movingimage. In addition, by appropriately adjusting or changing thearrangement pitch length, the pitch length B of the image 20 a, thewidth C in the arrangement direction of the cylindrical lenses of theimage 20 a, and the height D of the image 20 a, the size of the virtualimage to be observed based on the equations (1) to (3) mentionedhereinbefore can be freely set.

A plurality of images 21 a as images for observing virtual image areformed on an image forming layer 21 shown in FIG. 16B. The configurationof the image 21 a is substantially the same as or identical to that ofthe image 20 a, and hence, the explanation thereof is omitted herein.

A virtual image showing an arrow based on the image 21 a and thecylindrical lens, not shown, can be observed from an upper side of thelenticular sheet as a pseudo moving image. In addition, by appropriatelyadjusting or changing the arrangement pitch length, the pitch length Bof the image 21 a, the width C in the arrangement direction of thecylindrical lenses of the image 21 a, and the height D of the image 21a, the size of the virtual image to be observed based on the equations(1) to (3) mentioned hereinbefore can be freely set.

In a case where the pitch length B of the images 20 a (or 21 a), issmaller than the arrangement pitch A, not shown, of the flat cylindricallenses (A>B), a virtual image representing an arrow based on thecylindrical lenses and the images 20 a (or 21 a) will be observedstereoscopically in a going down fashion of the lenticular sheet by anobserver. In this case, when the line of sight of the observer is movedrightward, the virtual image representing an arrow is observed as isalso moved rightward, and on the other hand, when the line of sight ofthe observer is moved leftward, the virtual image representing an arrowis observed as is also moved leftward. That is, the virtual imagerepresenting an arrow is observed in the same direction as the movingdirection of the line of sight of the observer, and accordingly, it canbe effectively utilized for the induction in the advancing direction.

On the other hand, in the case the pitch length B of the images 20 a (or21 a) is larger than the arrangement pitch length A, not shown, of thecylindrical lenses (A<B), the virtual image representing an arrow basedon the cylindrical lenses and the images 20 a (or 21 a) will be observedstereoscopically in a going up fashion by the observer. In this case,the virtual image rotated by 180 degrees of the images 20 a (or 21 a)will be observed by the observer. And when the line of sight of theobserver is moved rightward, the virtual image representing an arrow isobserved as is moved leftward, and on the other hand, when the line ofsight of the observer is moved leftward, the virtual image representingan arrow is observed as is moved rightward. That is, the virtual imagerepresenting an arrow is observed in the direction reverse to the movingdirection of the line of sight of the observer and accordingly, it canbe effectively utilized for the induction in the direction reverse tothe advancing direction.

Other lenses may be provided above the lenticular sheet, which will beexplained hereunder with reference to the drawings accompanied.

Other Embodiment 7

An image display sheet of the other embodiment 7 has a structure inwhich other lenses are provided above a lenticular sheet. The otherlenses, for example, are flat convex lenses, meniscus lenses, Fresnellenses or like. It is further to be noted that descriptions of the sameor identical structure as or to that of the above-mentioned embodimentswill be omitted herein.

FIG. 17 is a view for explaining a structure of an image display sheetaccording to the other embodiment 7, and FIG. 17 is a sectional viewthereof. The image display sheet 600 is provided, as essentialcomponents, with a lenticular sheet 61, an image forming layer 63 and aflat convex lens 64 as another convex lens.

The lenticular sheet 61 is composed of a plurality of cylindrical lenses61 a arranged side by side. The image forming medium 62 is disposed to aside of the lenticular sheet 61 on which convex-shape of cylindricallenses is not formed, and the image forming layer 63 is formed on thelenticular sheet 61 side. The image forming layer 63 is a layer in whichimages 63 a of picture pattern or letter as images for observing avirtual image are printed or transferred. The image forming layer 63 isprovided for the image forming medium 62 on the lenticular sheet 61side.

A flat convex lens 64 is disposed to the lenticular sheet 61 on the sideof the cylindrical lenses 61 a having convex shape. The flat convex lens64 has a convex (protruded) shape on the side opposite to the lenticularsheet 61 (i.e., upper side in FIG. 17). Further, although a material forthe flat convex lens 64 is not limited to specific one, a transparentresin material such as glass, PET (polyethylene terephthalate), PP, PETG(glycol-denatured polyethylene terephthalate), acryl, acrylate seriesresin or like.

FIG. 18 is a sectional view showing an essential portion of thelenticular sheet for showing a focusing condition thereof. A focal pointby a single cylindrical lens 61 a is converged at a point below theimage forming layer 63. According to the functions of such cylindricallenses 61 a and the flat convex lens 64, the image display sheet of thepresent embodiment is constructed so that the focal point from the upperportion of the flat convex lens 64 accords with an image 63 a formed onthe image forming layer 63.

It is further to be noted that the other structure or configuration ofthe lenticular sheet 61 is substantially the same as that of thelenticular sheet 1 mentioned hereinbefore, and in addition, thestructure of the image forming medium 62 is substantially the same asthat of the image forming medium 2 mentioned hereinbefore, and thestructure of the image forming layer 63 is substantially the same asthat of the image forming layer 3 or image forming layer 6 mentionedhereinbefore.

As explained hereinabove, in the present embodiment, the flat convexlens 64 is provided as the other lens on the side of the cylindricallenses 61 a, at which the convex portions are formed, of the lenticularsheet 61 so that the focus accords with the image 63 a through the flatconvex lens 64 and the cylindrical lenses 61 a. According to sucharrangement, or structure, in a case when the position detection isperformed based on the virtual image by using the other lenses, itbecomes possible to finely adjust the position of the virtual image byfinely adjust the central position of the flat convex lens 64 to bedisplaced in parallel with the image display sheet 600. It is preventedfor an observer to directly touch the surface of the cylindrical lenses61 a of the lenticular sheet 61, thus attaining the function asprotecting member. In addition, in a case of a virtual image being aneye, in accordance with the shape of the flat convex lens 64, an imagedisplay sheet 600 visually and sensitively approximated to the eye maybe composed.

Further, in the example of FIG. 17, the flat convex lens 64 of the imagedisplay sheet 600 is constructed in a manner of being apart from thecylindrical lenses 61 a of the lenticular sheet 61 by a predetermineddistance, but in the present invention, the flat convex lens may bearranged in contact to the cylindrical lenses 61 a on the upper surfacethereof.

Although, with the other embodiment 7, there is explained an exampleusing the flat convex lens, the present invention is not limited to theflat convex lens. As long as it is possible to make the focus accordwith an image of the image forming layer by acting together with thecylindrical lens, for example, a convex-shaped glass plate, a plasticplate, meniscus lens, Fresnel lens or like may be used. Moreover, it maybe possible to form the image forming layer directly on the lenticularsheet in accordance with the other embodiment 2 mentioned hereinabove.In addition, it may be possible to constitute an image to be observed tobe capable of being observed in combination with a conventionally knownstereoscopic sheet in accordance with the other embodiment 3 mentionedhereinabove, a stereoscopic image, changing image or animation image, orcombination thereof.

Furthermore, it may be possible to use the flat convex lens inaccordance with the other embodiments 4 and 5 mentioned hereinabove.Still furthermore, although, in the other embodiment 7 mentioned above,it is constructed that the convex surface of the flat convex lens isopposed to the lenticular sheet (upper side in the drawing), it may bepossible to constitute such that the convex surface of the flat convexlens is faced to the lenticular sheet side (lower side in the drawing)as long as the focus makes coincident with the image of the imageforming layer in associated function with the cylindrical lens. In thecase when the flat convex lens is used in accordance with the otherembodiments 4 and 5 mentioned hereinbefore, it may be also possible toposition the convex surface of the flat convex lens to be opposed to theflat convex lens sheet or to face the flat convex sheet side.

Other Embodiment 8

An image display sheet according to the other embodiment is constitutedso that a virtual image smoothly moving in accordance with the line ofsight of an observer is to be made stationary. Further, the structuressame as or similar to those of the above-mentioned embodiments will beomitted in description herein.

FIG. 19A is a view explaining a structure of an image display sheetaccording to the other embodiment 8, which represents correspondencebetween a lenticular sheet 111 and respective cylindrical lenses 111 aand images 113 a, 113 b. Further, it is to be noted that the structureor arrangement of the lenticular sheet 111 is substantially the same asthat of the lenticular sheet 1, so that explanation thereof will beomitted herein.

On the image forming layer 113, a plural number of images 113 a and 113b as image groups for observation of virtual images (called group ofimage for observing virtual image, hereunder) are formed. The group ofimage for observing virtual image includes groups of the image forobserving stand still (stationary) virtual image which constituted by apredetermined number (for example, several tens) of images for observingstand still virtual image.

The image 113 b as the image for observing stand still virtual image isone constituting a virtual image to become stationary. In an example ofFIG. 19A, groups of image for observing stand still virtual imagecomposed of eight images 113 b are formed on both end portions of groupof image for observing virtual image for the sake of simplifiedillustration. The images 113 a and 113 b are formed in a repeated mannerso as to correspond to the cylindrical lenses 1 a substantiallyone-on-one.

The image 113 b will be explained hereunder. FIG. 19B is an explanationview of original images 113Xa and 113Xb. FIGS. 19C and 19D representexamples of preparation of group of image for observing stand stillvirtual image. Further, the image 113 a, which is not image forobserving stand still virtual image, in the images for observing virtualimage formed on the image forming layer 113 has the same or identicalstructure of the image 3 a mentioned hereinbefore, and hence, theexplanation thereof is omitted herein.

In the example of FIG. 19B, the image 113 b is composed of two elementsof black circle and white circle. The original image 113X of the image113 b is composed of an original image 113Xa as an origin of the blackcircle and an original image 113Xb as an origin of the white circle. Theimage 113 b includes a cut-out portion 113 c and an enlarged portion 113b respectively to the original images 113Xa and 113Xb, and then reducedin predetermined sizes.

Definition of a plurality of auxiliary lines to the original image 113Xwill be explained. For example, definitions of auxiliary lines 113 e fornumber of images 113 b constituting the group of image for observingstand still virtual image and auxiliary lines 113 e for preparing anenlarged portion 113 d to the image 113 b will be made. In the case ofFIG. 19A, the group of image for observing stand still virtual image atthe left end side of the image forming layer 113 is composed of siximages 113 b, and accordingly, six auxiliary lines 113 e and twoauxiliary lines 113 e forming the enlarged portion 113 d, i.e., totaleight auxiliary lines (113 e(1), 113 e(2), 113 e(8)) will be defined.The respective auxiliary lines are arranged with equal interval orirregular interval.

Further, the enlarged portion 113 d forming the image 113 b is formed onthe side of the image 113 a. Because of this reason, the image 113 bconstituting the group of image for observing stand still virtual imageon the left side of the image forming layer 113 forms the enlargedportion 113 d using the auxiliary line 113 e(1), and the image 113 bconstituting the group of image for observing stand still virtual imageon the right side of the image forming layer 113 forms the enlargedportion 113 d using the auxiliary line 113 e(8).

Therefore, since the image 113 b constituting the group of image forobserving stand still virtual image on the left side of the imageforming layer 113 does not use the auxiliary line 113 e(8), in theinitial stage, only the seven auxiliary lines 113 e(1) to 113 e(7) maybe defined. Likely, the image 113 b constituting the group of image forobserving stand still virtual image on the right side of the imageforming layer 113 does not use the auxiliary line 113 e(1), only theseven auxiliary lines 113 e(2) to 113 e(8) may be defined. For the sakeof simple explanation, a case in which eight auxiliary lines are drawnto the original image 113X will be explained regardless of the images113 b constituting the left or right group of image for observing standstill virtual image.

Further, herein, an example, in which two auxiliary lines 113 e(1) and113 e(8) forming the enlarged portion 113 d are made as tangential linesto the original image 113X, will be explained. Further, in thefollowings, the term auxiliary line 113 e may be used for explaining anyone of auxiliary lines 113 e(1) to 113 e(8) or all of them totally.

FIGS. 19C and 19D represent preparation examples of groups of image forobserving stand still virtual image, in which FIG. 19C represents apreparation example of the group of image for observing stand stillvirtual image on the left side of the image forming layer 113 shown inFIG. 19A, and FIG. 19D represents a preparation example of the group ofimage for observing stand still virtual image on the right side of theimage forming layer 113 shown in FIG. 19A. The groups of image forobserving stand still virtual image shown in FIGS. 19C and 19D will beexplained with reference to examples of cases formed respectively withsix images 113 b. Further, the auxiliary line 113 e and alater-mentioned intersection point P are for defining the cut-outportion 113 c and the enlarged portion 113 d, so that they are notdescribed on the image forming layer 113.

First, refereeing to FIG. 19C, the preparation example of the group ofimage for observing stand still virtual image on the left side of theimage forming layer 113 will be explained. At first, original images113X of the number corresponding to the number of the images 113 bconstituting the group of image for observing stand still virtual imageis prepared. In the example of FIG. 19C, six original images 113X areprepared (C-1). Further, in the examples of (C-1) and (C-2) of FIG. 19C,the original images 113X are illustrated with non-color (white) mannerfor the sake of clear observation.

The respective original images 113X are deformed based on vertical linedescribed to the auxiliary line 113 e(1) from the intersection pointsbetween the auxiliary lines 113 e(2) to 113 e(7) and the original images113X. In the example of FIG. 19C, as to the respective original images113X, the respective original images 113X are deformed based on verticalline described to the auxiliary line 113 e(1) from the intersectionpoints P between the auxiliary lines 113 e(2) to 113 e(7) and theoriginal images 113X (C-2). In the example of FIG. 19C, the originalimages 113X are composed of the original images 113Xa and 113Xb.

Accordingly, in the example of the original images 113Xa, the respectiveoriginal images 113Xa are deformed based on vertical line described tothe auxiliary line 113 e(1) from the intersection point P between theauxiliary lines 113 e(2) to 113 e(7) and the original images 113Xa. Inthe like manner, the respective original images 113Xb are deformed basedon vertical line described to the auxiliary line 113 e(1) from theintersection point P between the auxiliary lines 113 e(2) to 113 e(7)and the original images 113Xb.

More specifically, as to the original image 113X, nearest to the image113 a in the six original images 113X (most right-side original image113X in FIG. 19C), a vertical line is drawn to the auxiliary line 113e(1) from the two intersection points P of the auxiliary lines 113 e(2)and the original images 113Xa.

As to the original image 113X, secondarily nearest to the image 113 a inthe six original images 113X, a vertical line is drawn to the auxiliaryline 113 e(1) from the two intersection points P of the auxiliary lines113 e(3) and the original images 113Xa.

As to the original image 113X, thirdly nearest to the image 113 a in thesix original images 113X, a vertical line is drawn to the auxiliary line113 e(1) from the two intersection points P of the auxiliary lines 113e(4) and the original images 113Xa.

As to the original image 113X, fourthly nearest to the image 113 a inthe six original images 113X, a vertical line is drawn to the auxiliaryline 113 e(1) from the two intersection points P of the auxiliary lines113 e(5) and the original images 113Xa.

As to the original image 113X, fifthly nearest to the image 113 a in thesix original images 113X, a vertical line is drawn to the auxiliary line113 e(1) from the two intersection points P of the auxiliary lines 113e(6) and the original images 113Xa.

As to the original image 113X, sixthly nearest to the image 113 a in thesix original images 113X, i.e., the original image on the most left sideimage 113X in the drawing, a vertical line is drawn to the auxiliaryline 113 e(1) from the two intersection points P of the auxiliary lines113 e(7) and the original images 113Xa.

As mentioned hereinabove, the original image 113X is deformed based onthe auxiliary line 113 e(1) and the vertical line. In the example ofFIG. 19C (C-3), the original image 113X is deformed based on theauxiliary line 113 e(1) and the vertical line. The original image 113Xhas the enlarged portion 113 d on the image 113 a side (right side inFIG. 19C). More specifically, the enlarged portion 113 d is formed bythe auxiliary line 113 e(1) and the vertical line.

At least one or more images 113 b positioned on the left end side of thegroup of image for observing virtual image have cutouts 113 c formed atboth end portions in the vertical direction with respect to thearranging direction of the images 113 a and 113 b as virtual imageobservation images. In the example of FIG. 19C (C-3), in the case of theoriginal images 113Xa, when the auxiliary lines 113 e(2) to 113 e(7)having the intersection points P are positioned on the left side of thecentral portion (in other words, when they are positioned on the sideapart from the image 113 a than the central position of the originalimage 113Xa), the cutouts 113 c are formed above and below the originalimage 113Xa. In the like manner, in the case of the original images113Xb, when the auxiliary lines 113 e(2) to 113 e(7) having theintersection points P is positioned on the left side of the centralportion (in other words, when they are positioned on the side apart fromthe image 113 b than the central position of the original image 113Xb),the cutouts 113 c are formed above and below the original image 113Xb.

Further, the original images 113X after the deformation are downscaledin predetermined size to thereby form the images 113 b (C-4). In theexample of FIG. 19C (C-4), six images 113 b are formed.

Then, refereeing to FIG. 19D, the preparation example of the group ofimage for observing stand still virtual image on the right side of theimage forming layer 113 will be explained. At first, original images113X of the number corresponding to the number of the images 113 bconstituting the group of image for observing stand still virtual imageare prepared. In the example of FIG. 19D, six original images 113X areprepared (D-1). Further, in the examples of (D-1) and (D-2) of FIG. 19D,the original images 113X are illustrated with non-color (white) mannerfor the sake of clear observation.

The respective original images 113X are deformed based on vertical linedescribed to the auxiliary line 113 e(8) from the intersection pointsbetween the auxiliary lines 113 e(7) to 113 e(2) and the original images113X. In the example of FIG. 19D, as to the respective original images113X, the respective original images 113X are deformed based on verticalline described to the auxiliary line 113 e(8) from the intersectionpoints P between the auxiliary lines 113 e(7) to 113 e(2) and theoriginal images 113X (D-2). In the example of FIG. 19D, the originalimages 113X are composed of the original images 113Xa and 113Xb.Accordingly, the respective original images 113Xa are deformed based onvertical line described to the auxiliary line 113 e(8) from theintersection points P between the auxiliary lines 113 e(7) to 113 e(2)and the original images 113Xa. In the like manner, the respectiveoriginal images 113Xb are deformed based on vertical line described tothe auxiliary line 113 e(8) from the intersection points P between theauxiliary lines 113 e(7) to 113 e(2) and the original images 113Xb.

More specifically, as to the original image 113X, nearest to the image113 a in the six original images 113X (most left-side original image113X in FIG. 19D), a vertical line is drawn to the auxiliary line 113e(8) from the two intersection points P of the auxiliary lines 113 e(7)and the original images 113Xa.

As to the original image 113X, secondarily nearest to the image 113 a inthe six original images 113X, a vertical line is drawn to the auxiliaryline 113 e(8) from the two intersection points P of the auxiliary lines113 e(6) and the original images 113Xa.

As to the original image 113X, thirdly nearest to the image 113 a in thesix original images 113X, a vertical line is drawn to the auxiliary line113 e(8) from the two intersection points P of the auxiliary lines 113e(5) and the original images 113Xa.

As to the original image 113X, fourthly nearest to the image 113 a inthe six original images 113X, a vertical line is drawn to the auxiliaryline 113 e(8) from the two intersection points P of the auxiliary lines113 e(4) and the original images 113Xa.

As to the original image 113X, fifthly nearest to the image 113 a in thesix original images 113X, a vertical line is drawn to the auxiliary line113 e(8) from the two intersection points P of the auxiliary lines 113e(3) and the original images 113Xa.

As to the original image 113X, sixthly nearest to the image 113 a in thesix original images 113X, i.e., the most right side original image 113Xin the drawing, a vertical line is drawn to the auxiliary line 113 e(8)from the two intersection points P of the auxiliary lines 113 e(2) andthe original images 113Xa.

As mentioned hereinabove, the original image 113X is deformed based onthe auxiliary line 113 e(8) and the vertical line. In the example ofFIG. 19D (D-3), the original image 113X is deformed based on theauxiliary line 113 e(8) and the vertical line. The original image 113Xhas the enlarged portion 113 d on the image 113 a side (left side inFIG. 19D). More specifically, the enlarged portion 113 d is formed bythe auxiliary line 113 e(8) and the vertical line.

At least one or more images 113 b positioned on the right end side ofthe group of image for observing virtual image have cutouts 113 c formedat both end portions in the vertical direction with respect to thearranging direction of the images 113 a and 113 b as virtual imageobservation images. In the example of FIG. 19D (D-3), in the case of theoriginal images 113Xa, when the auxiliary lines 113 e(7) to 113 e(2)having the intersection points P is positioned on the right side of thecentral portion (in other words, when they are positioned on the sideapart from the image 113 a than the central position of the originalimage 113Xa), the cutouts 113 c are formed above and below the originalimage 113Xa. In the like manner, in the case of the original images113Xb, when the auxiliary lines 113 e(7) to 113 e(2) having theintersection points P are positioned on the right side of the centralportion (in other words, when they are positioned on the side apart fromthe image 113 a than the central position of the original image 113Xa),the cutouts 113 c are formed above and below the original image 113Xb.

Further, the original images 113X after the deformation are downscaledin predetermined size to thereby form the images 113 b (D-4). In theexample of FIG. 19D (D-4), six images 113 b are formed.

The group of image for observing stand still virtual image are formed onthe image forming layer 113 by the images 113 b formed by the mannermentioned above (FIG. 19A).

The images 113 a and 113 b are formed so as to correspond, one-on-one,to the cylindrical lenses 111 a as like as in the embodiments describedhereinbefore. It is constructed such that the arrangement pitch length Aof the cylindrical lenses 111 a differs from the ratio of differencebetween the pitch lengths B of the images 113 a and 113 b, and inaddition, the difference between the arrangement pitch length A of thecylindrical lenses 111 a and the pitch length B of the images 113 a isdifference is not more than 10%. Further, the pitch length B between theimage 113 a and the image 113 b, and the pitch length B between theimages 113 b are supposed to the pitch length B in a case of noformation of cutout 113 c and enlarged portion 113 d to the image 113 b.Moreover, the widths C and D are supposed to the widths C and D in acase of no cutout 113 c to the image 113 b.

Further, the image forming layer 113 may be formed to an image formingmedium, not shown, and also, as in another embodiment 2, may be formeddirectly to the lenticular sheet 111. In the case when the image forminglayer 113 is formed on the image forming medium, the image formingmedium has a structure or configuration identical to the image formingmedium 2 described hereinbefore.

As described hereinabove, since the image display sheet is formed so asto have the group of image for observing stand still virtual imagecomposed of a predetermined number of the images 113 b formed on the endportion of the group of image for observing virtual image and also havethe enlarged portion to the image 113 b, it becomes possible to stop(take stationary position) the virtual image 114 smoothly moving alongthe movement of the line of sight of an observer to the predeterminedposition. FIG. 20 is a view for explaining a configuration of a virtualimage, in which (A-1)˜(A-4) shows movement of the virtual image when theline of sight is moved rightward on the image display sheet 1100. Whenthe line of sight is moved rightward, the virtual image moves furtherrightward ((A-1)→(A-2)), and even if the line of sight is further movedrightward, the virtual image stops without further moving ((A-3) and(A-4)). (B-1)˜(B-4) shows movement of the virtual image when the line ofsight is moved leftward on the image display sheet 1100. When the lineof sight is moved leftward, the virtual image moves further rightward((B-1)→(B-2)), and even if the line of sight is further moved leftward,the virtual image stops without further moving ((B-3) and (B-4)). Asdescribed above, by constituting the group of image for observing standstill virtual image composed of the images 113 b, an image display sheetcapable of observing a stand still (stationary) virtual image can berealized.

Further, in the above-described embodiment, although there is explainedan example in which the auxiliary line 113 e(1) (FIG. 19C) and theauxiliary line 113 e(8) (FIG. 19D) forming the enlarged portion 113 dare tangential lines to the original image 113X, the present inventionis not limited to such example. FIG. 21 is a view for explaining anapplication of the other embodiment 9. In an example shown in FIG. 21,the auxiliary line 113 e(1) is defined at a position apart from theoriginal image 113X, and the original image 113X is deformed based onthe vertical line drawn to the auxiliary line 113 e(1) from theintersection point between the auxiliary lines 113 e(2) to 113 e(7) andthe original image 113X. As explained above, by defining the auxiliaryline 113 e(1) at the position apart from the original image 113X,further larger enlarged portion 113 d may be formed.

In the example shown in FIG. 19C, when the line of sight of an observeris moved leftward on the image display sheet 1100, the still virtualimage stops (i.e., is stationary). If the line of sight is further movedleftward after the stopping of the virtual image, the stopped virtualimage becomes invisible. However, with reference to an example of FIG.21, since the image 113 b has the larger enlarged portion 113 d, even ifthe line of sight is continuously moved after the stopping of thevirtual image, a virtual image can be observed for a time longer thanthe case of the image 113 b shown in FIG. 19C.

Furthermore, in the embodiment described above, although there isexplained an example in which the image 113 b having the cutout 113 cand the enlarged portion 113 b are formed by using the auxiliary lines113 e, the present invention is not limited to such example. In orderfor realizing the still (stationary) virtual image, the image 113 b asan image for observing stand still virtual image may be constituted soas to have at least the cutout 113 c and the enlarged portion 113 d.

Furthermore, in the embodiment described above, although there isadopted the structure having the groups of image for observing standstill virtual image composed of a predetermined number of images 113 bformed at both end portions of the group of image for observing virtualimage, there may adopt a structure in which the group of image forobserving stand still virtual image composed of the images 113 a isformed only one end portion thereof. For example, if a structure havingthe group of image for observing stand still virtual image formed on theleft side of the image 113 a in FIG. 19A is for example taken, there mayalso be adopted a structure in which when the line of sight is movedrightward on the image display sheet 1100, the virtual image 114 iscontinuously moved without being stopped, and when the line of sight ismoved leftward, the virtual image is moved leftward, and thereafter,stops.

Still furthermore, in the embodiment described above, although there isadopted the structure having the images 113 a as the images forobserving virtual image which are not the images for observing standstill virtual image to the image forming layer 113Xa, the presentinvention may be realized even in the case of no images 113 a.

Still furthermore, in the embodiment described above, although theexplanation is made to the manner or means in which the original images113Xa and 113Xb are reduced in the predetermined sizes after theformation of the cutouts 113 c and the enlarged portions 113 d, thepresent invention is not limited to such example, and after the originalimages 113Xa and 113Xb are reduced in the predetermined sizes, thecutouts 113 c and the enlarged portions 113 d may be formed.

Still furthermore, in the embodiment described above, although theoriginal images 113X are used as a manner or means for forming thecutouts 113 c and the enlarged portions 113 d, the present invention isnot limited to such example, and other formation means may be adopted asfar as the cutout 113 c and the enlarged portion 113 d can be formed tothe image 113 b.

(Embodiment of Position Detection System)

Hereunder, a case in which the image display sheets explained in theabove-mentioned respective embodiments are utilized for positiondetection is explained. In the present embodiment, there is explained acase, as an example of a position detection system, in which an imagedisplay sheet is attached to an object to be observed, this imagedisplay sheet is photographed, and a positional relationship between theobject to be observed and a camera is detected.

FIG. 22A is a schematic view showing a position detection system S1 towhich the image display sheet according to the present invention isapplicable. The position detection system S1 operates to photograph animage display sheet 1000 attached to an object to be observed 3000 by acamera 2000 provided to a robot or like, not shown, after attaching theimage display sheet 1000 to the object 3000. The photographed image istaken into a position detecting device 2002 constituted by a computer orlike from the camera 2000 through a cable 2001. With the image takeninto the position detecting device 2002, a photographed image of aportion of the image display sheet 1000 is extracted from an imageobtaining portion 2003, and an operating portion 2004 operates relativepositional relationship between the object to be observed 3000 and thecamera 2000 based on a virtual image imaged in the photographed image,and then, detects the position of the object 3000.

The image display sheet 1000 may take any structure as long as thestructure is a structure of one of the image display sheets explained inthe above-mentioned embodiments or combination thereof, but herein, animage display sheet constituted to be capable of observing a virtualimage by using a flat convex lens sheet as one example.

FIG. 22B is a sectional view of the image display sheet 1000, and is aview explaining correspondence between a flat convex lens 101 a andimages 103A and 103B. In the image forming layer 103, a plurality ofimages 103A and 103B as virtual image observation images are formed bymeans of printing or transcription. The images 103A and 103B arearranged repeatedly so as to accord one-on-one with the flat convexlenses 101 a, respectively. It is further to be noted that the imagedisplay sheet 1000 explained in this embodiment has the same pitch ofthe image 103A in the perpendicular (vertical) and transverse(horizontal) (x-direction and y-direction) of the flat convex lens 101a, and also has the same pitch of the image 103B in the perpendicular(vertical) and transverse (horizontal) of the flat convex lens 101 a.The other structures of the image display sheet 1000 are identical tothose of the image display sheet 500, and accordingly, the explanationthereof will be omitted herein.

A virtual image 104A based on the flat convex lens 101 a and the image103A and a virtual image 104B based on the image 103B are observed andphotographed. The respective pitch lengths of the flat convex lenses 103a have relationship represented by the equations (4) to (7). When theposition of the camera 2000 changes (i.e., is moved) in the x-directionwith respect to the object 3000 to be observed, images corresponding tovirtual images 104A and 104B are moved in the x-direction andphotographed. And when the position of the camera 2000 changes (i.e., ismoved) in the y-direction with respect to the object 3000 to beobserved, images corresponding to virtual images 104A and 104B are movedin the y-direction and photographed. Accordingly, the virtual image 104Abased on the image 103A is moved faster in the virtual image movementaccording to the position movement of the camera than that of thevirtual image 104B based on the image 103B (equation 8). According tosuch structure, the virtual images 104A (+mark) 104B (◯mark)respectively having different performance (displacement) with respect tothe displacement of the angle θ, at which the object to be observed canbe visually observed, can be observed on the image display sheet 1000.Then, it is preferred to set the respective pitches of the flat convexlenses 103 a and the images 103A, 103B in accordance with the desiredpositional detection performance.

[Formula 2]

Pitch length of image 103A<arrangement pitch length of flat convex lens101a  equation (4)

Pitch length of image 103B<arrangement pitch length of flat convex lens101a  equation (5)

Pitch length of image 103B<pitch length of image 103A  equation (6)

|Pitch length of flat convex lens 101a−pitch length of image103A|<|Pitch length of flat convex lens 101a−pitch length of image103B|  equation (7)

Moving speed of virtual image 104B<moving speed of virtual image104A  equation (8)

FIG. 23A is a view explaining the camera position and the photographedimage, and photographed images 2005 (x (−1)), 2005 (x (0)) and 2005 (x(1)) are images extracted at the image obtaining portion 2003photographed by the camera 2000. In the photographed image 2005 (x (0)),photographed by the camera 2000 at the position (camera position 2000 (x(0)), perpendicular to the image display sheet 1000 (angle θ=0), thevirtual images 104A and 104B are overlapped at the center of the images.When the camera 2000 is moved in the x-direction (camera position 2000(x (1)) and the camera position 2000 (x (−1)), the virtual images 104Aand 104B in the photographed image 2005 (x (−1)) are also moved in thesame direction as the moving direction of the camera.

The operating portion 2004 operates the relative positional relationshipin the x-direction between the object 3000 to be observed and the camera2000 based on the difference Δx between the position of the virtualimage 104A and the position of the virtual image 104B, and then, detectsthe position of the camera 2000.

The same will be applied to the case of the y-direction. FIG. 23B is aview for explaining the camera position and the photographed image andis the explanatory view relating to the y-directional movement of thecamera position. In the photographed image 2005 (y (0)), photographed bythe camera 2000 at the position (camera position 2000 (y (0)),perpendicular to the image display sheet 1000 (angle θ=0), the virtualimages 104A and 104B are overlapped at the center of the images. Whenthe camera 2000 is moved in the y-direction (camera position 2000 (y(1)) and the camera position 2000 (y (−1)), the virtual images 104A and104B in the photographed image 2005 (−1)) are also moved in the samedirection as the moving direction of the camera. The operating portion2004 operates the relative positional relationship in the y-directionbetween the object 3000 to be observed and the camera 2000 based on thedifference Δy between the position of the virtual image 104A and theposition of the virtual image 104B, and then, detects the position ofthe camera 2000.

Further, in the above explanation, although there is explained the casein which the pitch of the image 103A is the same in the perpendiculardirection and horizontal direction (x-direction and y-direction) of theflat convex lens 101 a, and the pitch of the image 103B is the same inthe perpendicular direction and horizontal direction of the flat convexlens 101 a, the images may be constituted so as to provide the differentpitches. Moreover, herein, although the camera position is detected bythe difference Δx between the two virtual images, in the case of onevirtual image, the camera position may be detected based on thedifference in the moving distance from the reference position of thephotographed image 2005 (x (0) (or photographed image 2005 (y (0)) atthe camera position 2000 (x (0) or (camera position 2000 (y 0). Thereference position is, for example, is the center of the photographedimage, four corners, reference guide (explained hereinafter) or like.The same will be applied in the descriptions hereunder.

As can be understood from the above-mentioned descriptions, it will befound that the image display sheet 1000 provided for the object 3000 tobe observed for the position detection can be utilized for the positiondetection system S1. That is, with the image display sheet 1000, aplurality of images 103A and 103B for displaying the virtual images 104Aand 104B in reaction to the flat convex lenses 101 a are formed to theimage forming layer 103 one-on-one in the repeated manner, thearrangement pitch length of the flat convex lens 101 a in the horizontaldirection and the pitch length of the image in the horizontal directionare different within the range less than 10%, the arrangement pitchlength of the flat convex lens 101 a in the perpendicular direction andthe pitch length of the image in the perpendicular direction of theimages 103A and 104B are different within the range less than 10%, andthe virtual images 104A and 104B smoothly moving with respect to thedisplacement of the angle θ for visually observing the object to beobserved can be observed. The image display sheet 1000 is light weightand in shape of sheet, and hence, even if the object 3000 to be observedis a small member (for example, mere several cm), it can be used bybonding the image display sheet 1000 of small size (for example, severalmm square), so that it can be used as a position detection referencehaving high space-saving performance. In addition, by using a repeatedlydetachable bonding agent, the image display sheet may be constituted tobe freely detachable.

Further, according to the structure mentioned above, although the cameraposition is detected by the two virtual images 104A and 104B havingdifferent performance moving in the same direction as that of thecamera, it may be possible to detect the camera position by the virtualimage moving in the direction reverse to the same moving direction ofthe virtual image as the moving direction of the camera. For example, byconstituting the pitch length of the image 103B is made larger than thearrangement pitch length of the flat convex lens 101 a, the virtualimage 104B based on the flat convex lens 101 a and the image 103B can beobserved and photographed. Herein, when the position of the camera 2000changes (is moved) in the forward direction in the y-direction withrespect to the object 3000 to be observed, the image 104B isphotographed as an image moved in the reverse direction in they-direction is photographed.

FIG. 23C is a view for explaining the camera position and thephotographed image, and is an explanatory view relating to the movementin the x-direction of the camera position in the case of using the imagedisplay sheet in which two virtual images of which moving directions aredifferent from each other can be observed. The photographed images 2005(x (−1)), 2005 (x (0)) and 2005 (x (1)) are images extracted at theimage obtaining portion 2003 photographed by the camera 2000. When thecamera 2000 is moved in the x-direction (camera position 2000 (x (1))and the camera position 2000 (x (−1)), the virtual image 104A (+mark) ismoved in the same direction as the moving direction of the camera, andthe virtual image 104B (◯mark) is moved in the direction reverse to themoving direction of the camera. The operating portion 2004 operates therelative positional relationship in the x-direction between the object3000 to be observed and the camera 2000 based on the difference Δxbetween the position of the virtual image 104A and the position of thevirtual image 104B, and then, detects the position of the camera 2000.The same operation will be referred to the y-direction.

FIG. 23D is a view for explaining the camera position and thephotographed image, and is an explanatory view relating to the movementin the y-direction of the camera position in the case of using the imagedisplay sheet in which two virtual images of which moving directions aredifferent from each other can be observed. When the camera 2000 is movedin the y-direction (camera position 2000 (y (1)) and the camera position2000 (−1)), the virtual image 104A (+mark) in the photographed image2005 (y (−1)) is moved in the same direction as the moving direction ofthe camera, and the virtual image 104B (◯mark) is moved in the directionreverse to the moving direction of the camera. The operating portion2004 operates the relative positional relationship in the y-directionbetween the object 3000 to be observed and the camera 2000 based on thedifference Δy between the position of the virtual image 104A and theposition of the virtual image 104B, and then, detects the position ofthe camera 2000.

In comparison with the case when the virtual images 104A and 104Bdescribed above are moved in the same direction (shown in FIG. 23A andFIG. 23B), even in a case of less moving amount of the camera, sincelarge positional differences Δx and Δy are obtained, the more accuratecamera position detection can be realized.

FIG. 24A represents one example of a photographed image, and thisexample is the photographed image 2005 (x (−1), y (1)) in the case wherethe camera position is moved in an A-direction (−1 in the x-directionand 1 in the y-direction) in the case of using the image display sheetfrom which two virtual images of which moving directions are differentfrom each other can be observed (FIG. 23C, FIG. 23D).

FIGS. 24B to 24E are views representing examples of photographed imagesin a case of using an image display sheet of another structure. Forexample, it is possible to detect whether or not the camera position isout of a predetermined range based on a photographed image. The pitch ofthe virtual image on the image display sheet is determined based on theequation (1). Because of this reason, the pitch of the virtual image canbe constructed so that a plurality of virtual images based on the sameimages in the photographed image 2005 at the first time when the cameraposition takes the predetermined position. FIG. 24B is one example ofthe photographed image 2005 in which two virtual images are confirmed.In the case when the image 2005 of FIG. 24B is photographed, it is foundout that the camera position departs from the predetermined position inthe y-direction. Since it can be detected instantaneously that thecamera departs from the predetermined position without waitingquantitative calculation of the camera position by the operating portion2004, it can be applicable to the improvement in high safety of a robot,not shown, to which the camera 2000 is provided.

Any kind of mark for a virtual image may be available. Hereinbefore,although the examples of the cases using two marks of the (+mark) andthe (◯mark) are explained, two marks (+mark) of the virtual images suchas shown in FIG. 24C may be available. In such case, one of the virtualimage of (+mark) and the other of the virtual image of (+mark) areconstructed to be discriminant. For example, the virtual images areconstructed in a manner such that the two virtual images have differentmoving amounts (performance, speed) with respect to the displacement ofthe angle with which the object 3000 to be observed is visuallyconfirmed, or have difference moving directions with respect to thedisplacement of the angle with which the object 3000 to be observed isvisually confirmed. Further, these two virtual images may be constructedwith different shapes (sizes) or different colors, or may be combined.

Furthermore, a reference guide may be provided to the image displaysheet 1000. FIG. 24D is a plan view of the image display sheet 1000 towhich a reference guide 2006 is provided. The reference guide 2006 islocated on the side at which the flat convex lens 101 a of the imagedisplay sheet 1000 has the convex shape. Further, if the reference guide2000 could be observed from the convex-shape side of the flat convexlens 101 a, the located position of the reference guide would not bespecified. In the case when the reference guide 2000 itself has nostrain by the action of the lens, the reference guide may be locatedinside or below the flat convex lens, or even if some strain exists, aslong as the strain is within a predetermined allowable range, thereference guide may be located inside or below the flat convex lens. Inaccordance with the positional relationship between the virtual image104A and the reference guide 2006, the camera position can becalculated.

Another example of the reference guide 2006 is shown in FIG. 24E. Thereference guide 2006, may be provided as measurement guide line as shownin FIG. 24E. If one division of the measurement guide line is determinedto a time when the camera position is moved in the x- (or y-) direction,a user can be instantaneously specifies the camera position based on thephotographed image provided for the user without making any operation bythe operating portion 2004.

Further, at the time when the image obtaining portion 2003 extracts thepart of the image display sheet from the image obtained by the camera2000, it may be made to overlap an image (reference guide image)corresponding to the reference guide and display the same on the displayportion, not shown, or provide one printed by a printer, not shown, to auser. The user grasps the movement of the camera based on the providedvirtual image 104A imaged on the photographed image and the referenceguide 2006, or specifies quantitatively the camera position.

With the position detection system S1, although the image display sheetusing the flat convex lens was explained as an example, it may bepossible to use an image display sheet using a lenticular sheet as aposition detection system. The specific structure of the image displaysheet to be used is the structure explained with reference to the aboveembodiments.

FIG. 25 is a schematic view showing a position detection system S2 towhich the image display sheet according to the present invention isapplicable. An image display sheet 4000A using a lenticular sheet inwhich cylindrical lenticular lenses are arranged in the x-direction andan image display sheet 4000B using a lenticular sheet in whichcylindrical lenticular lenses are arranged in the y-direction areattached to an object 3000 to be observed. The structure other than theabove is the same as that of the position detection system S1, so thatthe explanation thereof will be omitted herein. With the image displaysheet 4000A, two virtual images 104A(A) and 104B(A) having differentcharacteristics can be observed, and the camera position in thex-direction can be operated based on the positional difference Δxbetween the two virtual images 104A(A) and 104B(A) observed in the imagedisplay sheet 4000A. With the image display sheet 4000B, two virtualimages 104A(B) and 104B(B) having different characteristics can beobserved, and the camera position in the y-direction can be operatedbased on the positional difference Δy between the two virtual images104A(B) and 104B(B) observed in the image display sheet 4000A. Twovirtual images 104A(A) and 104B(A) and two virtual images 104A(B) and104B(B) observed respectively in the image display sheets 4000A and4000B are moved with different performance (moving amount) and/or indifferent directions with respect to the displacement of the angle θwith which the object 3000 can be visually observed.

In the case when it is desired to detect only the relative position inthe x-direction of the object 3000 to be observed and the camera 2000,only the image display sheet 4000B may be attached to the object 3000 tobe observed.

According to the structures mentioned hereinabove, the positiondetection system S2 can use the image display sheet 4000A (image displaysheet 4000B) as the image display sheet 4000A (4000B), in which aplurality of images for displaying the virtual images in coaction withthe cylindrical lenses are formed on the image forming layer in arepeated manner so as to be correspond to the respective cylindricallenses one-on-one, the arrangement pitch length of the cylindricallenses and the pitch length of the images formed repeatedly on the imageforming layer differs from each other in a range of not more than 10%,and the virtual images 104A(A) and 104B(B) smoothly moving with respectto the displacement of the angle for visually observing the object 3000to be observed can be observed. In the case when the only one virtualimage is provided for corresponding one image display sheet 4000A(4000B), the camera position will be detected based on the difference inthe moving distance of the reference position of the photographed image.The reference position is, for example, the center of the image, fourcorners thereof, reference guide, or like. The position for providingthe reference guide is not limited as long as being viewed from the sideon which the convex shape of the cylindrical lens is formed.

Consequently, the respective embodiments explained by using FIGS. 1 to25 may be combined for the structure of the image display sheet.Furthermore, although the respective embodiments shows examples in whichthe lenticular sheets or flat convex lens sheets contact the imageforming mediums forming the image forming layers, respectively, thepresent invention is not limited to such examples, and it may bepossible to arrange the lenticular sheet or flat convex lens sheet andthe image forming medium forming the image forming layer separately by apredetermined distance. Furthermore, it may be also possible tointerpose an optional medium which does not obstruct a predeterminedpseudo moving image display between the lenticular sheet or flat convexlens sheet and the image forming medium forming the image forminglayers.

The applicable range of the present invention is not limited to theembodiments described hereinbefore. The present invention is widelyapplicable to image display sheets performing the position detection bydisplaying the pseudo moving image. For example, the image displaysheets of the present invention can be applied to the position detectionof various kinds of working robots such as medical robot, industrialrobot, and the like.

REFERENCE NUMERAL

-   -   100, 200, 300, 400, 500, 600, 1000, 4000A, 4000B—image display        sheet    -   1, 5, 8, 10, 61, 71—lenticular sheet    -   1 a, 5 a, 8 a, 10 a, 61 a—cylindrical lens    -   2, 8, 11, 16, 62, 102—image forming medium    -   3, 6, 9, 12, 13, 17, 19, 20, 21, 63, 103—image forming layer    -   3 a, 6 a, 6 b, 12 a, 17 a, 19 a, 19 b, 20 a, 21 b, 63 a, 103A,        103B—image (image for observing virtual image)    -   113 b—image (image for observing virtual image, image for        observing stand still virtual image)    -   13 a, 13 b—image (other image)    -   6 c, 19 c, 113 c—cutout    -   113 d—enlarged portion    -   4, 7, 18, 114, 104A, 104B, 104A(A), 104 b(A), 104A(B),        104B(B)—virtual image    -   15, 101—flat convex lens sheet    -   15 a, 101 a—flat convex lens    -   64—flat convex lens (other convex lens)    -   2000—camera,    -   2002—position detecting device    -   2005—photographed image    -   2006—reference guide

1. An image display sheet, which is provided for an object to beobserved for position detection and constituted by laminating alenticular sheet composed of arrangement of a plurality of cylindricallenses and an image forming layer, and in which an image formed on theimage forming layer from a convex shape side of the cylindrical lensesof the lenticular sheet is formed to be observable as virtual imageprovided with movement, or movement and deformation, wherein thelenticular sheet has a predetermined thickness so that the image forminglayer is positioned on a focal surface of the cylindrical lenses, aplurality of images for observing virtual images for displaying singleor a plurality of the virtual image in association with the cylindricallenses are formed repeatedly on the image forming layer so as tocorrespond to the cylindrical lenses respectively one-on-one, anarrangement pitch length of the cylindrical lenses and a pitch length ofthe image for observing virtual image formed repeatedly on the imageforming layer differs in a range of not more than 10%, the image forobserving the virtual image is an image reduced in size in thearrangement directions of the cylindrical lens of the virtual image asan object to be observed and the image for observing the virtual image,and the virtual image smoothly moving with respect to displacement of anangle at which the object is visually observed is thereby observed. 2.An image display sheet, which is provided for an object to be observedfor position detection and constituted by laminating a flat convex lenssheet composed of arrangement of a plurality of flat convex lenses andan image forming layer, and in which an image formed on the imageforming layer from a convex shape side of the flat convex lenses of theflat convex lens sheet is formed to be observable as virtual imageprovided with movement, or movement and deformation, wherein the flatconvex lens sheet has a predetermined thickness so that the imageforming layer is positioned on a focal surface of the flat convexlenses, a plurality of images for observing virtual images fordisplaying single or a plurality of the virtual image in associationwith the cylindrical lenses are formed repeatedly on the image forminglayer so as to correspond to the cylindrical lenses respectivelyone-on-one, a plurality of images for observing virtual images fordisplaying single or a plurality of the virtual image in associationwith the flat convex lenses is formed repeatedly on the image forminglayer so as to correspond to the flat convex lenses respectivelyone-on-one, an arrangement pitch length in a horizontal direction of theflat convex lenses and a pitch length in a horizontal direction of theimage for observing virtual image formed repeatedly on the image forminglayer differs in a range of not more than 5%, and an arrangement pitchlength in a vertical direction of the flat convex lenses and a pitchlength in a vertical direction of the image for observing virtual imageformed repeatedly on the image forming layer differs in a range of notmore than 5%, and the virtual image smoothly moving with respect todisplacement of an angle at which the object is visually observed isthereby observed.
 3. The image display sheet according to claim 1,wherein the image display sheet is provided with a reference guide thatis observable from a side having convex shape of the cylindrical lens.4. The image display sheet according to claim 1, wherein a plurality,not less than two kinds, of images for observing the virtual imageshaving different pitch lengths are formed on the image forming layerrepeatedly substantially one-on-one with respect to the cylindricallenses, and a plurality of virtual images having at least onecharacteristic of different moving amount or different moving directionwith respect to the displacement of an angle at which the object isvisually observable is observable.
 5. The image display sheet accordingto claim 1 wherein a plurality, not less than two kinds, of images forobserving the virtual images having different shapes or colors areformed on the image forming layer repeatedly substantially one-on-onewith respect to the cylindrical lenses, and a plurality of virtualimages having at least one characteristic of different shape anddifferent color is observable.
 6. The image display sheet according toclaim 2 wherein the image display sheet is provided with a referenceguide that is observable from a side having convex shape of the flatconvex lens.
 7. The image display sheet according to claim 2, wherein aplurality, not less than two kinds, of images for observing the virtualimages having different pitch lengths are formed on the image forminglayer repeatedly substantially one-on-one with respect to the flatconvex lenses, and a plurality of virtual images having at least onecharacteristic of different moving amount or different moving directionwith respect to the displacement of an angle at which the object isvisually observable is observable.
 8. The image display sheet accordingto claim 2 wherein a plurality, not less than two kinds, of images forobserving the virtual images having different shapes or colors areformed on the image forming layer repeatedly substantially one-on-onewith respect to the flat convex lenses, and a plurality of virtualimages having at least one characteristic of different shape.